Stochastic two-scale convergence in the mean and applications

Journal fur die Reine und Angewandte Mathematik

Volumn 1994, Issue 456, 1994, Pages 19-52

  Bourgeat, Alain ^a   Mikelić, Andro ^b   Wright, Steve ^c  

^a UNIVERSITÉ JEAN MONNET   (France)

^b UNIVERSITÉ LYON 1   (France)

^c OAKLAND UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84942225190     PISSN: 00754102     EISSN: 14355345     Source Type: Journal    
DOI: 10.1515/crll.1994.456.19     Document Type: Article

References (24)

1. G. Allaire, Homogeneisation et convergence a deux echelles, C.R. Acad. Sci. Paris 312 (1991), 581–586.
2. G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal. 23 (1992), 1482–1518.
3. A. Bensoussan, J. L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures, North-Holland, Amsterdam 1978.
4. A. Bourgeat and A. Mikelić, Homogenization of the non-Newtonian flow through a porous medium, Nonlin. Anal. TMA, to appear.
5. A. Bourgeat and A. Mikelić, A note on the homogenization of Bingham flow through a porous medium, J. Math. Pures Appl. 72 (1993), 405–414.
6. G. Dal Maso and L. Modica, Nonlinear stochastic homogenization, Ann. Mat. pura appl. (IV) 144 (1986), 347–389.
7. G. Dal Maso and L. Modica, Nonlinear stochastic homogenization and ergodic theory, J. reine angew. Math. 368 (1986), 28–42.
8. J. Diestel and J.J. Uhl Jr. Vector measures, Amer. Math. Soc., Providence 1977.
9. J. L. Doob, Stochastic processes, John Wiley and Sons, New York 1990.
10. N. Dunford and J. T. Schwartz, Linear operators, Part I, John Wiley and Sons, New York 1963.
11. P. R. Halmos, Measure theory, Van Nostrand, New York 1950.
12. E. Hewitt and K. Stromberg, Real and abstract analysis, Springer-Verlag, New York-Heidelberg-Berlin 1969.
13. E. Hille and R.S. Phillips, Functional analysis and semigroups, Amer. Math. Soc., Providence 1957.
14. U. Hornung, W. Jager and A. Mikelić, Reactive transport through an array of cells with semi-permeable membranes, M2AN 28 (1994), 59–94.
15. S. M. Kozlov, Averaging random structures, Soviet Math. Dokl. 19 (1978), 950–954.
16. S. M. Kozlov, Averaging of random operators, Math. U.S.S.R. Sbornik 37 (1980), 167–180.
17. F. Murat, Compacite par compensation, Ann. Sc. Norm. Sup. Pisa (4) 5 (1978), 485–507.
18. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal. 20 (1989), 608–623.
19. G. C. Papanicolaou and S.R.S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, Proceedings of a colloquium on random fields: rigorous results in statistical mechanics and quantum field theory, Colloq. Mat. Soc. J. Bolyai, North-Holland, Amsterdam 1979.
20. M. Reed and B. Simon, Methods of modern mathematical physics, Vol. 1, Functional Analysis, Academic Press, New York 1980.
21. W. Rudin, Functional Analysis, McGraw-Hill, New York 1973.
22. V. V. Zhikov, S. M. Kozlov and O.A. Oleinik, Averaging of parabolic operators, Trans. Moscow Math. Soc. 45 (1984), 189–241.
23. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik and K.T. Ngoan, Averaging and G-convergence of differential operators, Russian Math. Surv. 34 (1979), 69–147.
24. V. V. Zhikov, S. M. Kozlov and O. A. Oleinik, Homogenization of differential operators, Springer-Verlag 1994.